Details

analyze59.0ms (1.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (41.9%)

Symmetry

(sort a x)

Results

761.0ms	1528×	body	2048	valid
564.0ms	1799×	body	1024	valid
278.0ms	3145×	body	128	valid
253.0ms	1155×	body	512	valid
101.0ms	629×	body	256	valid
13.0ms	147×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
455×	`*-commutative_binary64`
440×	`unswap-sqr_binary64`
344×	`associate-l_binary64`
274×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	16	6
2	23	6
3	35	6
4	70	6
5	160	6
6	432	6
7	1564	6
8	3490	6
9	4954	6
10	4993	6
11	4874	6

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(expm1.f64 (*.f64 a x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`log1p-expm1-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (*.f64 a x))

simplify67.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
844×	`distribute-lft-out_binary64`
785×	`fma-neg_binary64`
383×	`*-commutative_binary64`
308×	`unswap-sqr_binary64`

Counts

35 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	382
1	96	369
2	262	363
3	966	347
4	2376	333
5	3696	333
6	4842	333
7	5375	333

prune12.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	16	3	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	4	20

Error

0.0b

Counts

20 → 4

Alt Table

Status	Error	Program
	25.7b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	0.8b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	15.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

Compiler

Compiled 307 to 149 computations (51.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	0.3b	(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	11.1b	(cbrt.f64 (expm1.f64 (*.f64 a x)))

series1.1s (22.6%)

Counts

3 → 72

Calls

3 calls:

609.0ms

(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

483.0ms

(cbrt.f64 (expm1.f64 (*.f64 a x)))

7.0ms

(*.f64 (*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

4.0ms

(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

1.0ms

(cbrt.f64 (expm1.f64 (*.f64 a x)))

simplify127.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
437×	`*-commutative_binary64`
358×	`distribute-rgt-in_binary64`
343×	`distribute-lft-in_binary64`
260×	`unswap-sqr_binary64`

Counts

165 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	168	2948
1	409	2621
2	1154	2203
3	2637	2016
4	4849	1965
5	4962	1965
6	4932	1965

prune128.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	264	2	266
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	265	5	270

Error

Counts

270 → 5

Alt Table

Status	Error	Program
	25.7b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
✓	0.0b	(expm1.f64 (*.f64 a x))
	15.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
	38.5b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (exp.f64 (log.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))))
▶	12.2b	(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2) 1/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))

Compiler

Compiled 6913 to 1953 computations (71.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (expm1.f64 (*.f64 a x)) 2)
✓	0.2b	(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2) 1/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	11.1b	(cbrt.f64 (expm1.f64 (*.f64 a x)))
✓	20.5b	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 2) 1/3)

series603.0ms (12.4%)

Counts

3 → 72

Calls

3 calls:

583.0ms	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 2) 1/3)
13.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 2)
7.0ms	(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2) 1/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`unpow-prod-down_binary64`
31×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

3 → 95

Calls

3 calls:

7.0ms	(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2) 1/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))
2.0ms	(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 2) 1/3)
1.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 2)

simplify147.0ms (3%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-def_binary64`
458×	`*-commutative_binary64`
438×	`distribute-rgt-in_binary64`
401×	`distribute-lft-in_binary64`
303×	`unswap-sqr_binary64`

Counts

167 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	3318
1	426	3050
2	1226	2694
3	2772	2662
4	4956	2662
5	4991	2662
6	5030	2662

prune119.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	193	5	198

Error

Counts

198 → 5

Alt Table

Status	Error	Program
	25.7b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	15.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
	38.5b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (exp.f64 (log.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))))
✓	12.2b	(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2) 1/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))

Compiler

Compiled 4702 to 2168 computations (53.9% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.2b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	15.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

series29.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
7.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 48

Calls

2 calls:

2.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
1.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)

simplify84.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

674×	`associate-l_binary64`
587×	`associate-r_binary64`
337×	`log-prod_binary64`
288×	`fma-def_binary64`
278×	`exp-prod_binary64`

Counts

96 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1262
1	202	1199
2	629	1177
3	3098	1171
4	4791	1171
5	4962	1171

prune54.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	89	5	94

Error

Counts

94 → 5

Alt Table

Status	Error	Program
	25.7b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
✓	0.0b	(expm1.f64 (*.f64 a x))
✓	15.6b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
	38.5b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (exp.f64 (log.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))))
✓	12.2b	(.f64 (pow.f64 (pow.f64 (expm1.f64 (.f64 a x)) 2) 1/3) (cbrt.f64 (expm1.f64 (*.f64 a x))))

Compiler

Compiled 1341 to 711 computations (47% saved)

regimes45.0ms (0.9%)

Accuracy

Total 0.0b remaining (39.5%)

Threshold costs 0.0b (39.5%)

Counts

10 → 1

Compiler

Compiled 710 to 379 computations (46.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
2	6	6

end102.0ms (2.1%)

Remove: (sort a x)
Compiler: Compiled 88 to 53 computations (39.8% saved)

Details

analyze59.0ms (1.2%)

sample2.0s (41.9%)

simplify70.0ms (1.4%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series7.0ms (0.1%)

rewrite1.0ms (0%)

simplify67.0ms (1.4%)

prune12.0ms (0.2%)

localize8.0ms (0.2%)

series1.1s (22.6%)

rewrite18.0ms (0.4%)

simplify127.0ms (2.6%)

prune128.0ms (2.6%)

localize9.0ms (0.2%)

series603.0ms (12.4%)

rewrite16.0ms (0.3%)

simplify147.0ms (3%)

prune119.0ms (2.5%)

localize5.0ms (0.1%)

series29.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify84.0ms (1.7%)

prune54.0ms (1.1%)

regimes45.0ms (0.9%)

simplify2.0ms (0%)

end102.0ms (2.1%)

Profiling